In a standard free end nonsmooth control problem in finite dimensional state space, a nonsmooth maximum principle is proved, in which the adjoint inclusion is sharper than the usual one. For end constrained problems, the same result holds, provided conditions ensuring local controllability are satisfied. The adjoint inclusion is expressed by means of a type of generalized gradient of the pseudo...

We present a version of the Pontryagin maximum principle for general infinitehorizon optimal control problem with an additional specific asymptotic endpoint constraint under weak regularity assumptions. Such problems arise in economics when studying growth models. The proof is based on reducing original to family finite-horizon mixed type functional containing terminal term form conditional cos...

The target of this paper is to draw attention to some important relations between different procedures of state space synthesis of discrete linear systems optimizing the quadratic cost function. Common form of the synthesis concerns one-dimensional and multi-dimensional control problems solved by Second Method of Lyapunov, Maximum Principle of Pontryagin and by Bellamn's Dynamic Programming. Em...

We study optimal control problems for general unstructured nonlinear differential-algebraic equations of arbitrary index. In particular, we derive necessary conditions in the case of linear-quadratic control problems and extend them to the general nonlinear case. We also present a Pontryagin maximum principle for general unstructured nonlinear DAEs in the case of restricted controls. Moreover, ...

Reach set computation is a basic component of many veri cation and control synthesis procedures. E ective computation schemes are available for discrete systems described by nite state machines and continuous-variable systems described by linear di erential inequalities. This paper suggests an approach based on the Pontryagin maximum principle of optimal control theory. The approach is elaborat...